ABSTRACT

Engineering problems can be broadly categorized into four general areas: direct problems, inverse problems, systems identification problems and research problems. The method of cross validation will allow us to optimally estimate parameters by using the data and only the data itself. Cross validation is based on the idea of removing one of the data points from the set and then solving the inverse problem using all of the remaining data points. In the case of the inverse problem, the smoothing parameter is the only remaining model parameter. The value of the smoothing parameter that minimizes the predicted errors is the optimal one. The origin of the ordinary cross validation estimate is considered important. It requires solving a set of some related optimization problems. The author shows how the dynamic programming approach provides a natural setting for the application of generalized cross validation to the general inverse problem.